First you have to get out a pail some rags ,rubber gloves and a scrub brush. First you start with the counters and work your way down.I like to use comet or Ajax /w bleach,if that doesn't take care of the black spots and grime there's something wrong.a s.o.s pad is helpful with really tough spots but remember their ebrasive so be careful not to scratch up everything,just use them on the worst spots and not on large areas,as for the brass fixtures use brasso it works the best of all metal cleaners and it shines it up real good too.last but not least for the limescale use C.L.R with the right cleaning supplies and a little hard work you should be able to get it clean enough to live with,if this stuff doesn't work my only advice is to rip out all the bad and totally replace every thing,toilet tub/shower ,tile,if you can't get it clean enough to be comfortable living with it redo it because you have to shower and use the toilet and if its not clean how can you get clean any way its better to put in the effort to get it clean than to redo it because it costs a lot less to get a couple of bottles of cleaner and use a little elbow grease then to replace everything unless of course you have that kind of money then by all means replace it all.
Baking soda instead of cleanser.
vinegar instead of bleach.
these 2 will clean anything and without chemicals.